a. Field
The present application discloses a number of methods, materials and devices that relate to reducing group velocities of phonons traveling within an at least partially crystalline base material. One purpose for group velocity reductions, for example, may be to reduce thermal conductivity; another may be to improve the thermoelectric energy conversion figure of merit.
b. Background
The thermoelectric effect refers to the ability to generate an electric current from a temperature difference between one side of a material and another. Conversely, applying an electric voltage to a thermoelectric material can cause one side of the material to heat while the other side stays cool, or, alternatively, one side to cool down while the other stays hot. Devices that incorporate thermoelectric materials have been used in both ways: to create electricity from a heat source or to provide cooling or heating by consuming electricity. To date, thermoelectric devices have been limited to niche or small-scale applications, such as providing power for the Mars Curiosity Rover or the cooling of precision instruments.
The widespread use of thermoelectric materials has been hindered by the problem that materials that are good electrical conductors also tend to be good conductors of heat. This means that at the same time a temperature difference creates an electric potential, the temperature difference itself begins to dissipate, thus weakening the current it created. Materials that have both high electrical conductivity, σ, and high thermal conductivity, κ, behave poorly in converting a temperature difference to an electric potential. In order for a material to perform well as a thermoelectric material, it should possess a high value of the figure of merit, ZT=(S2σ/κ)T, where S is the Seebeck coefficient, and T is the temperature.
In the past, scientists have tackled this problem by searching for materials with intrinsic properties that allow the conduction of electricity to take place more easily than the conduction of heat. More recently, nanotechnology has been utilized by material scientists to engineer nanostructured materials that would exhibit the properties desired. The utilization of nanostructuring for control of heat transport has been a rapidly growing area of research. Researchers have tried various schemes to reduce heat transport in thermoelectric materials, such as introducing holes, inclusions, particles, interfaces and/or grains of other materials into a thermoelectric material in order to scatter the phonons (carriers of heat), but these tend to reduce the transport of electric current as well (because they scatter the electrons), which negated the improvement.
The manipulation of elastic waves in a macroscale periodic medium (i.e., with unit-cell size in the order of hundreds of micrometers or higher) can be realized primarily in two distinct ways: (i) the utilization of Bragg-scattering phononic crystals and (ii) the introduction of local resonances. The latter renders the medium a “metamaterial.” The concept of a phononic crystal involves a material with an artificial periodic internal structure for which the lattice spacing has a length scale on the order of the propagating waves. In such a configuration, wave interferences occur across the unit cell providing a unique frequency band structure with the possibility of band gaps. The concept of a metamaterial, on the other hand, generally involves the inclusion of local resonators (i.e., mechanical oscillators) which enable unique subwavelength properties to emerge. While periodicity is advantageous in some implementations, it is not necessary in a metamaterial. At a macroscale (where the focus is on acoustics or mechanical vibrations), periodic locally resonant metamaterials have been considered in various forms, such as by having heavy inclusions coated with a compliant material (e.g., rubber-coated lead spheres) and hosted in a relatively lighter and less stiff matrix (e.g., epoxy) Z. Y. Liu, X. X. Zhang, Y. W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan, and P. Sheng, Science 289, 1734 (2000), or by the presence of pillars on a plate Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, Phys. Rev. B 78, 104105 (2008); T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, Appl. Phys. Lett. 93, 111902 (2008).
In recent years, the concept of a phononic crystal has been applied to the problem of nanoscale phonon (thermal) transport. In this context, the periodic material can be realized in a variety of ways such as by the layering of multiple constituents, also known as a layered superlattice M. N. Luckyanova, J. Garg, K. Esfarjani, A. Jandl, M. T. Bulsara, A. J. Schmidt, A. J. Minnich, S. Chen, M. S. Dresselhaus, Z. F. Ren, E. A. Fitzgerald, and G. Chen, Science 338, 936 (2012), or the introduction of inclusions and/or holes, as in a nanophononic crystal (NPC) J. Tang, H.-T. Wang, D. H. Lee, M. Fardy, Z. Huo, T. P. Russell, and P. Yang, Nano Lett. 10, 4279 (2010); J. K. Yu, S. Mitrovic, D. Tham, J. Varghese, and J. R. Heath, Nat. Nanotechnol. 5, 718 (2010). To date, the notion of a locally resonant phononic (or elastic or acoustic) metamaterial has been limited to macroscale problems where the interest and applicability is in mechanical vibrations or acoustics (as opposed to thermal transport and heat transfer).